Reversible Conservative Rational Abstract Geometrical Computation Is Turing-Universal
In Abstract geometrical computation for black hole computation (MCU ’04, LNCS 3354), the author provides a setting based on rational numbers, abstract geometrical computation, with super-Turing capability. In the present paper, we prove the Turing computing capability of reversible conservative abstract geometrical computation. Reversibility allows backtracking as well as saving energy; it corresponds here to the local reversibility of collisions. Conservativeness corresponds to the preservation of another energy measure ensuring that the number of signals remains bounded. We first consider 2-counter automata enhanced with a stack to keep track of the computation. Then we built a simulation by reversible conservative rational signal machines.
KeywordsAbstract geometrical computation Conservativeness Rational numbers Reversibility Turing-computability 2-counter automata
Unable to display preview. Download preview PDF.
- [DL05a]Durand-Lose, J.: Abstract geometrical computation 1: embedding black hole computations with rational numbers. Research Report RR-2005-05, LIFO, U. D’Orléans, France (2005), http://www.univ-orleans.fr/lifo/prodsci/rapports
- [DM02]Delorme, M., Mazoyer, J.: Signals on cellular automata. In: [Ada02], pp. 234–275 (2002)Google Scholar
- [JSS02]Jakubowsky, M.H., Steiglitz, K., Squier, R.: Computing with solitons: a review and prospectus. In: [Ada 2002], pp. 277–297 (2002)Google Scholar